Hi Howard
I would certainly not describe myself as an expert on these matters, I talk generally from experience and my understanding+some assumptions (hopefully correct).
My background is electronics, having served an apprentiship at the Royal Aircraft Establishment at Farnborough + computing/iT, however I have always had an interest in all things mechanical, as my father was a precision engineer/toolmaker, designing among other things pressure transducers as used on the 'Tornado' fighter. He was responsible for my interest in all things mechanical, despite me having had no formal training or tuition in the field.
Anyway - I digress.......
The reasoning I have re the the 3.44 diff opposed to the 3.88 goes as follows.
Take the diff scenario to the extreme with 2 diff's being used on the same car on level ground, one 1:1 and the other 10:1. I would expect the 10:1 diff to offer very little build up of torque on the gearbox quill shaft (ie,flywheel to gearbox), the mechanical advantage of the 10:1 diff would 'light the tyres up' easily although top speeds would be very low. Whereas the 1:1 diff would be a sod to get moving with, without the mechanical assistance, you'd either have to dump the clutch at high rpm, and hope! or slip the clutch causing excess wear and a slow take up.
High torque motors would make getting moving at lower revs easier, but again, would load the quill shaft up more on the mechanically challenged 1:1 as opposed to the assisting 10:1. I know I have used extremes but that is how I see it, I have driven cars of similar power with 3.88 diff's and 3.44 diffs, the 3.88's seem to accelerate more quickly but run out of steam earlier so you need to shift earlier/more often. Of course, once you break traction, the motor's availability of additional power/torque becomes irrelevant as it is then being 'wasted' anyway.
Derek Bell's conversion for the UN1 was good in many ways, it made the input shaft one piece and a min of 1" dia or more from end to end, plus gave longer ratios for both 1st and second gear - very useful for getting an advantage out of slow corners if you have enough motor to use it.
Finally (cos I'm rambling now) - add slick tyres to the equation. With them as sticky as possible on a hot day, the 3.44 then still generates a higher load on the quill that the 3.88 at any given rpm. When Roy's quill broke, we were hard on the throttle in 4th, on slicks, at about 4000rpm.
We (read me - oop's) have only ever broken one drive shaft to date. As I regularly started in 2nd on Roy's car, to avoid the shift from 1st to 2nd and as his motor was happy with it, it should have been easy-peasy at Gurston Down hill climb, especially as the start points you 'down-hill'.
However, as I approached the start line I returned to 1st by mistake and realising this, I selected what I thought was second, oop's I selected 4th in my haste, so really the driveshaft had little chance, 2000rpm, get the bite and as the clutch engages 'floor-it' - BANG! - my mistake, driver error, but still the Derek Bell parts survived unscathed!
Not wanting to tempt fate, there has NOT BEEN ONE FAILURE of a Derek Bell conversion to date that I am aware of.
So that is how I see it, hopefully the many more 'mechanically knowledgeable' among the forum members /ubbthreads/images/graemlins/flehan.gif will be able to explain the above in more scientific terms and more hopefully, prove what I've said is NOT a load of 'twaddle' - but if they do - then what the hell, at least I continue to learn.. /ubbthreads/images/graemlins/smile.gif